Question

Find a fraction equivalent to 5/7 whose squared terms add up to 1184.

Answer 1

The system of equations of two unknowns is formulated and solved.

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ (x)/(y) = (5)/(7) \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=(5)/(7)y } \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left ((5)/(7)y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^(2)=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^(2)=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm√(784)=\pm28 } \end{gathered}$}`

`\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=(5)/(7)(\pm 28)=\pm 20 } \end{gathered}$}`

The fraction that satisfies the request is
`\bf{(20)/(28)}` , since in
`\bf{(-20)/(-28)}` the negative signs are canceled and the first fraction is obtained.